CN114589701B - Damping least square-based multi-joint mechanical arm obstacle avoidance inverse kinematics method - Google Patents

Abstract

The invention discloses a damping least square based multi-joint mechanical arm obstacle avoidance inverse kinematics method. Comprising the following steps: establishing a D-H joint coordinate system according to the structure of the multi-joint mechanical arm, and then solving the coordinate conversion relation and the jacobian matrix of the positive kinematics of the multi-joint mechanical arm; calculating the total virtual repulsive force of the obstacle to each connecting rod in the multi-joint mechanical arm according to the relative position relation between the obstacle and each connecting rod in the multi-joint mechanical arm and the coordinate conversion relation of the positive kinematics of the multi-joint mechanical arm; and finally, based on a damping least square method, establishing an inverse kinematics optimization objective function of the multi-joint mechanical arm according to the jacobian matrix and the virtual repulsive force, and solving the inverse kinematics optimization function of the multi-joint mechanical arm by adopting a numerical iteration method to obtain the angles of all joints corresponding to the terminal pose of the multi-joint mechanical arm. According to the invention, the obstacle avoidance planning and the inverse kinematics solving process of the mechanical arm are fused, the flow of an obstacle avoidance method is simplified, and the real-time performance of obstacle avoidance of the mechanical arm is ensured.

Description

An inverse kinematics method for obstacle avoidance of multi-joint manipulator based on damped least squares

Technical Field

The invention relates to an inverse kinematics method of a multi-joint manipulator, belonging to the field of manipulator kinematics, and specifically relates to an inverse kinematics method of a multi-joint manipulator obstacle avoidance based on damped least squares.

Background technique

A multi-joint robot is a type of redundant robot. In addition to the three position degrees of freedom and three posture degrees of freedom, it also has more redundant degrees of freedom, which leads to the self-motion characteristics of the multi-joint robot, that is, each joint can still move while ensuring that the end position is fixed. Therefore, this type of robot has high movement flexibility and can complete obstacle avoidance while the end position remains unchanged, which is very suitable for working in complex environments.

The first step in obstacle avoidance for a multi-joint robotic arm is to solve the inverse kinematics. Due to the great redundancy of degrees of freedom, the analytical solution of the inverse kinematics of a multi-joint robotic arm often does not exist. Even if an analytical solution exists, it is often accompanied by multiple solutions that are difficult to screen. Considering the complexity of the inverse kinematics of a multi-joint robotic arm, the current common inverse kinematics solution methods generally do not consider obstacle constraints.

Summary of the invention

In order to overcome the difficulties caused by the redundant degrees of freedom of a multi-joint manipulator, make full use of the flexibility of the multi-joint manipulator under the obstacle avoidance requirements, and improve the operating performance of a multi-joint manipulator with redundant degrees of freedom in a complex environment, the present invention provides a multi-joint manipulator obstacle avoidance inverse kinematics method based on damped least squares. Aiming at the real-time obstacle avoidance problem of a multi-joint manipulator during movement, the present invention designs the inverse kinematics optimization function of the manipulator based on the damped least squares method given the end position of the manipulator, the spatial coordinates of the obstacle, and the size of the obstacle, and uses iterative solution to obtain the joint angle that ultimately meets the obstacle avoidance conditions, thereby simplifying the complexity of the multi-joint manipulator obstacle avoidance method.

To achieve the above purpose, the specific contents of the technical solution of the present invention are as follows:

The present invention comprises the following steps:

Step 1: Establish a D-H joint coordinate system according to the structure of the multi-joint robotic arm, and obtain the coordinate transformation relationship and Jacobian matrix of the forward kinematics of the multi-joint robotic arm based on the D-H joint coordinate system;

Step 2: According to the relative position relationship between the obstacle and each link in the multi-joint robotic arm and the coordinate transformation relationship of the forward kinematics of the multi-joint robotic arm, the total virtual repulsion of the obstacle on each link in the multi-joint robotic arm is calculated;

Step 3: Based on the damped least squares method, the inverse kinematics optimization objective function of the multi-joint robotic arm is established according to the Jacobian matrix and the virtual repulsion. The numerical iteration method is used to solve the inverse kinematics optimization function of the multi-joint robotic arm to obtain the joint angles corresponding to the end posture of the multi-joint robotic arm.

The second step is specifically as follows:

2.1) According to the relative position relationship between the obstacle and the connecting rod in the multi-joint robot arm and the coordinate transformation relationship of the forward kinematics of the multi-joint robot arm, calculate the direction of the virtual repulsive force of each obstacle on each connecting rod in the multi-joint robot arm and the corresponding virtual repulsive force potential energy;

2.2) After multiplying the direction of the virtual repulsion of each obstacle on the current link in the multi-joint robotic arm and the corresponding virtual repulsion potential energy, the virtual repulsion of each obstacle on the current link in the multi-joint robotic arm is obtained, and then the virtual repulsions are summed to obtain the total virtual repulsion of the obstacle on the current link in the multi-joint robotic arm;

2.3) Repeat 2.1)-2.2) to calculate and obtain the total virtual repulsion of the obstacle on the remaining links in the multi-joint robotic arm.

The direction of the virtual repulsive force of each obstacle on each link in the multi-joint robotic arm is determined by the relative position between the obstacle and the link, specifically:

According to the direction of the virtual repulsive force of obstacle k on connecting rod i, the distances OP _{A and} OP _B between the geometric center O of obstacle k and the two end points PA and _{PB of connecting rod i, and the relationship between the axis PA and PB formed by} connecting the two end points PA _{and PB} of connecting rod i can be divided into the following three cases:

When the projection of the geometric center O of obstacle k on the axis P _A P _B of connecting rod i is located on the extension line of one side of P _B , the spatial distance d _ik from obstacle k to connecting rod i satisfies d _ik ＝|OP _B |-Rr _k , R is the radius of the circle where the end of connecting rod i is located, r _k is half of the maximum diameter of the obstacle, and the direction of the virtual repulsive force is

When the projection of the geometric center O of obstacle k on the axis P _A P _B of connecting rod i is located on the extension line of one side of P _A , the spatial distance d _ik from obstacle k to connecting rod i satisfies d _ik ＝|OP _A |-Rr _k , and the direction of the virtual repulsive force is

When the projection of the geometric center O of obstacle k on the axis P _A P _B of connecting rod i is located between the axes P _A P _B , the spatial distance d _ik from obstacle k to connecting rod i satisfies d _ik ＝|OP _v |-Rr _k , and the direction of the virtual repulsive force is

The calculation formula of the virtual repulsive potential energy of each obstacle on the current link in the multi-joint robotic arm is as follows:

Where, _Eik represents the virtual repulsive potential energy of obstacle k acting on link i, _kr is the obstacle repulsion coefficient, _d0 is the impact distance of the obstacle, and _dik is the spatial distance from obstacle k to link i;

In the third step, the formula of the inverse kinematics optimization objective function of the multi-joint robotic arm is:

Where J is the Jacobian matrix of the multi-joint robot, F _force (q) represents the cumulative force of the virtual repulsion on the joint, f _force (q) is the component of the virtual repulsive force on the connecting rod, q represents the joint angles of the multi-joint robot, λ ² represents the regularization term coefficient, x represents the end position of the multi-joint robot, ‖‖ represents the two-norm operation, min represents the minimum operation, and γ is the repulsive force decay coefficient related to the number of iterations p.

In the third step of solving the inverse kinematics optimization objective function by using the numerical iteration method, the updated terminal posture is obtained by adjusting each joint angle q. The posture residual is calculated according to the updated terminal posture and the preset terminal posture ^0TE _. After minimizing the posture residual, the final joint angle q is obtained. The formula in the solution process is as follows:

H _p =(J _p ^T J _p +λ ² I) ^-1

γ＝σ ^p

Where H _p is the Hessian matrix at the p-th iteration, J _p is the Jacobian matrix at the p-th iteration, e _p is the pose residual at the p-th iteration, λ ² is the regularization term coefficient, tr() represents the operation of converting the homogeneous matrix into a vector form, and γ is the repulsion decay coefficient related to the number of iterations p; represents the positive kinematic relationship, σ is the single-step repulsion force decay coefficient, T represents the transposition operation, and q _p and q _p+1 represent the joint angles at the pth and p+1th iterations, respectively.

Adjacent connecting rods of the multi-joint mechanical arm are connected by universal joints.

Compared with the prior art, the present invention has the following beneficial effects:

1. An inverse kinematics method for a multi-joint robotic arm is proposed. When the basic information of the robotic arm (number of joints, length of each joint, etc.) and obstacle information (spatial position and size) are known, the robotic arm joint angle combination that meets the obstacle avoidance conditions can be obtained, making full use of the redundant degrees of freedom of the multi-joint robotic arm to meet the needs of obstacle avoidance operations.

2. Taking into account the relative positions of various obstacles and the robot arm connecting rod, a virtual repulsion expression based on potential energy is proposed, and a virtual repulsion expression with clear physical meaning is defined to ensure the safety of multi-joint robot arm operation in the presence of obstacles.

3. The damped least squares equation taking into account the virtual repulsion is solved using a numerical iteration method, which still meets the accuracy and real-time performance of the inverse kinematics solution when the equation has no analytical solution.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the appearance of a multi-joint robotic arm;

Fig. 2 is a flow chart of the method steps;

Fig. 3 is a schematic diagram of coordinate system definition;

FIG4 is a schematic diagram of obstacle distance calculation;

FIG5 is a diagram of the obstacle avoidance process of a multi-joint robotic arm demonstrated in Matlab of the present invention;

FIG. 6 is a diagram showing the position error results of the multi-joint robot arm end in a Matlab simulation experiment of the present invention.

Detailed ways

The solution process of the present invention is described in more detail below with reference to examples and drawings.

In this embodiment, the connecting rod sequence number of the multi-joint robotic arm is i=1, 2, ..., I, which is arranged in sequence from the base outward, with a total number of I. Each connecting rod is cylindrical in shape, with a length of L and a radius of R. The connecting rods are connected by universal joints, as shown in Figure 1.

For the universal joint at the i-th link of the robot arm, two mutually perpendicular rotation angles θ _i , Describe the two rotational degrees of freedom of the universal joint. For the coordinate system {O-xyz} at the center of the universal joint, the rotation angle around the z-axis is θ _i , and the rotation angle around the y-axis is / > As shown in Figure 3, the joint angle can be defined as/>

As shown in FIG. 2 , the present invention comprises the following steps:

Step 1: Establish a D-H joint coordinate system according to the structure of the multi-joint robotic arm, and obtain the coordinate transformation relationship and Jacobian matrix of the forward kinematics of the multi-joint robotic arm based on the D-H joint coordinate system;

In the specific implementation, a DH coordinate system {O _n -x _n y _n z _n } is established at the center of the universal joint, where n=1,2,…,N represents the sequence number of the rotational degrees of freedom, and N=2I, that is, each universal joint has two rotational degrees of freedom in perpendicular directions. The coordinate definition at the universal joint is shown in FIG3 .

The forward kinematics of a robotic arm can usually be expressed as the following function:

It shows that the position of the end effector ξ _E is a function of the joint angle q. According to the DH method, using homogeneous transformation, its expression will be a simple product of the transformation matrix of a single link, and the coordinate transformation relationship of the forward kinematics can be obtained as follows:

ξ _E ～ ⁰ _TE ＝ ⁰ A ₁ · ¹ A ₂ … ^n-1 A _n

in, is a 4×4 homogeneous matrix, consisting of a rotation matrix R _3×3 and a translation vector T _3×1 . ^n-1 A _n is the transformation matrix between DH coordinate systems, which can be expressed as:

Where q _n , α _n , a _n , d _n are the parameters describing the robot arm link in the DH method.

At the same time, in order to facilitate the subsequent inverse kinematics analysis, it is also necessary to find the Jacobian matrix of the robot arm, which is in the form of:

The Jacobian matrix can be obtained by differentiating the formula of the forward kinematics of the robot.

Step 2: According to the relative position relationship between the obstacle and each link in the multi-joint robotic arm and the coordinate transformation relationship of the forward kinematics of the multi-joint robotic arm, the total virtual repulsion of the obstacle on each link in the multi-joint robotic arm is calculated;

The second step is as follows:

2.1) According to the relative position relationship between the obstacle and the connecting rod in the multi-joint robot arm and the coordinate transformation relationship of the forward kinematics of the multi-joint robot arm, calculate the direction of the virtual repulsive force of each obstacle on each connecting rod in the multi-joint robot arm and the corresponding virtual repulsive force potential energy;

The direction of the virtual repulsive force of each obstacle on each link in the multi-joint robot arm is determined by the relative position between the obstacle and the link, specifically:

Regarding the direction of the virtual repulsive force of obstacle k on connecting rod i, as shown in FIG4 , the distances OP _A and OP _B between the geometric center O of obstacle _k and the two end points PA and _PB of connecting rod i, and the relationship between the axes _PA and _PB formed by connecting the two end points PA _{and PB} of connecting rod i can be divided into the following three cases, among which, the positions _PA and _PB of the front and rear end points of connecting rod i can be obtained by calculating the transformation matrix between DH coordinate systems and the coordinate transformation relationship of forward kinematics:

As shown in (a) of Figure 4, when the projection of the geometric center O of obstacle k on the axis P _A P _B of connecting rod i is located on the extension line of one side of P _B , that is, |OP _B | ² + | _{PAPB |} ² ≤ |OP _A | ² , the spatial distance d _ik from obstacle k to connecting rod i satisfies d _ik ＝|OP _B |-Rr _k , where R is the radius of the circle where the end of connecting rod i is located, and _rk is half of the maximum diameter of the obstacle. The direction of the virtual repulsive force is The corresponding virtual repulsion E _f satisfies/>

As shown in (b) of Figure 4, when the projection of the geometric center O of obstacle k on the axis P _A P _B of connecting rod i is located on the extension line of one side of P _A , that is, |OP _A | ² +|P _A P _B | ² ≤|OP _B | ² , the spatial distance d _ik from obstacle k to connecting rod i satisfies d _ik ＝|OP _A |-Rr _k , and the direction of the virtual repulsive force is The corresponding virtual repulsion E _f satisfies/>

As shown in (c) of Figure 4, when the projection of the geometric center O of the obstacle k on the axis P _A P _B of the connecting rod i is located between the axes P _A P _B , the spatial distance d _ik from the obstacle k to the connecting rod i satisfies d _ik = |OP _v |-Rr _k , and the direction of the virtual repulsive force is The corresponding virtual repulsion E _f satisfies/>

The calculation formula of the virtual repulsive potential energy of each obstacle on the current link in the multi-joint robot arm is as follows:

Wherein, _Eik represents the virtual repulsive potential energy of obstacle k acting on connecting rod i, _kr is the obstacle repulsion coefficient, _d0 is the influence distance of the obstacle, and _dik is the spatial distance from obstacle k to connecting rod i. In the specific implementation, it is assumed that the obstacle is set in the enclosing sphere, the geometric center position of the obstacle is the center of the enclosing sphere, the maximum diameter of the obstacle is the diameter of the enclosing sphere, the radius of the enclosing sphere is _rk , and the connecting rod is cylindrical, that is, _dik represents the spatial distance between the cylindrical connecting rod and the enclosing sphere.

2.2) After multiplying the direction of the virtual repulsion of each obstacle on the current link in the multi-joint robotic arm and the corresponding virtual repulsion potential energy, the virtual repulsion of each obstacle on the current link in the multi-joint robotic arm is obtained, and then the virtual repulsions are summed to obtain the total virtual repulsion of the obstacle on the current link in the multi-joint robotic arm;

In the specific implementation, all virtual repulsive forces are vector-added, and then the virtual repulsive forces are transformed to the coordinate systems of each joint through coordinate transformation. ^0RB is the rotation matrix of point _PB in the base coordinate system. The transformation matrix _TB of point _PB can be obtained by the _coordinate transformation relationship of positive kinematics and decomposed to obtain the total virtual repulsive force _Ei of the obstacle on the link i in space:

E _i ＝ ⁰ _RB ^-1 ·∑E _ik

The posture of each link i is given by θ _i , Two joint angles are controlled, thus acting on θ _i ,/> Joint repulsion are the components of E _i on the y-axis and z-axis respectively, so the joint repulsion force vector of link i is:

2.3) Repeat 2.1)-2.2) to calculate and obtain the total virtual repulsion of the obstacle on the remaining links in the multi-joint robotic arm.

The inverse kinematics solution of the robot arm is to obtain the joint angles given the end pose matrix ξ _E The process is expressed as:

In the third step, based on the damped least squares method, considering the influence of virtual repulsion on the joints, the formula of the inverse kinematics optimization objective function of the multi-joint manipulator is:

Where J is the Jacobian matrix of the multi-joint robot, F _force (q) represents the cumulative force of the virtual repulsion on the joint, f _force (q) is the component of the virtual repulsive force acting on the connecting rod, q represents the angles of each joint of the multi-joint robot arm, and λ ² represents the regularization term coefficient. In this embodiment, / > This can make the final posture error smaller. x represents the end position of the robot, ‖‖ represents the operation of taking the two norms, min represents the operation of taking the minimum value, and γ is the repulsive force decay coefficient used for iterative solution. It is related to the number of iterations p and gradually decreases during the iteration process. The specific form is shown below. The formula of the optimization objective function shows that the influence of repulsion should be minimized while the tracking trajectory error and joint velocity norm of the end of the robot are minimized. For multi-joint robot arms, this can make the multi-joint robot arm posture obtained by inverse kinematics solution farther away from obstacles and joint limit positions.

In the third step, the numerical iteration method is used to solve the inverse kinematics optimization objective function. The updated end position is obtained by adjusting the joint angle q. T represents the transposition operation, which makes the updated end pose approach the preset end pose continuously. The pose residual is calculated according to the updated end pose and the preset end pose ⁰ T _E. After the pose residual is minimized during iteration, in the specific implementation, when the pose residual is less than the preset threshold, that is, the pose residual is minimized, the iteration is stopped, and the final joint angle q is obtained. The formula in the solution process is as follows:

H _p =(J _p ^T J _p +λ ² I) ^-1

γ＝σ ^p

Wherein, H _p is the Hessian matrix at the p-th iteration, J _p is the Jacobian matrix at the p-th iteration, _ep is the pose residual at the p-th iteration, satisfying _ep = [dv _x , dv _y , dv _z , dω _x , dω _x , dω _z ] ^T , dv _x , dv _y , dv _z represent the position residuals on the x, y, and z axes respectively, dω _x , dω _x , dω _z represent the angle residuals on the x, y, and z axes respectively, λ ² is the regularization term coefficient, tr() represents the operation of converting the homogeneous matrix into a vector form, γ is the repulsive force decay coefficient related to the number of iterations p, which decreases with the number of iterations, σ is the single-step repulsive force decay coefficient, a constant, σ∈(0,1), and σ=0.5 in this embodiment; represents the positive kinematics relationship, T represents the transpose operation, and _qp and _qp+1 represent the joint angles at the pth and p+1th iterations, respectively.

In the first few iterations, f _force (q) guides the joint to quickly move away from obstacles or joint limit positions to avoid the influence of local minimum values. In the later stages of the iteration, the coefficient γ of f _force (q) approaches 0, which makes the iteration converge to the target pose more quickly, thus ensuring the convergence of the improved algorithm.

The Matlab simulation obstacle avoidance process diagram of the present invention is shown in (a)-(d) of FIG5 . It can be seen that the multi-joint manipulator successfully avoids obstacles when the obstacles move and can follow the desired end position. As shown in (a) and (b) of FIG6 , the error between the actual and expected end positions is less than 10 ^-10 meters, and the error between the actual and expected end angles is less than 10 ^-10 rad, which meets the accuracy of the inverse kinematics solution.

Claims (5)

1. The damping least square based multi-joint mechanical arm obstacle avoidance inverse kinematics method is characterized by comprising the following steps of:

the first step: establishing a D-H joint coordinate system according to the structure of the multi-joint mechanical arm, and solving a coordinate conversion relation and a jacobian matrix of the positive kinematics of the multi-joint mechanical arm based on the D-H joint coordinate system;

and a second step of: calculating the total virtual repulsive force of the obstacle to each connecting rod in the multi-joint mechanical arm according to the relative position relation between the obstacle and each connecting rod in the multi-joint mechanical arm and the coordinate conversion relation of the positive kinematics of the multi-joint mechanical arm;

and a third step of: based on a damping least square method, establishing an inverse kinematics optimization objective function of the multi-joint mechanical arm according to the jacobian matrix and the virtual repulsive force, and solving the inverse kinematics optimization function of the multi-joint mechanical arm by adopting a numerical iteration method to obtain each joint angle corresponding to the terminal pose of the multi-joint mechanical arm;

in the third step, the formula of the inverse kinematics optimization objective function of the multi-joint mechanical arm is as follows:

wherein J is a jacobian matrix of the multi-joint mechanical arm, F _force (q) represents the cumulative force of the virtual repulsive force on the joint,f _force (q) is the component of the virtual repulsive force acting on the link, q represents the respective joint angles of the multi-joint mechanical arm, λ ² The method comprises the steps of representing a regular term coefficient, wherein x represents the tail end position of a multi-joint mechanical arm, min represents a two-norm operation, min represents a minimum operation, and gamma is a repulsive force fading coefficient related to the iteration times p;

said third stepIn the solving process of solving the inverse kinematics optimization objective function by adopting a numerical iteration method, the updated terminal pose is obtained by adjusting the angle q of each joint, and the updated terminal pose and the preset terminal pose are used according to the updated terminal pose ⁰ T _E Calculating pose residual errors, and obtaining final joint angles q after the pose residual errors are minimized, wherein the formula in the solving process is as follows:

e _p ＝tr( ⁰ T _E -κ(q _p ))

H _p ＝(J _p ^T J _p +λ ² I) ^-1

γ＝σ ^p

wherein H is _p Is the Hessian matrix at the p-th iteration, J _p Is the jacobian matrix at the p-th iteration, e _p Is the pose residual error at the p-th iteration, lambda ² Is a regular term coefficient, tr () represents an operation of converting the homogeneous matrix into a vector form, and γ is a repulsive force decay coefficient related to the number of iterations p; kappa () represents a positive kinematic relationship, sigma is a single-step repulsive decay coefficient, T represents a transpose operation, q _p 、q _p+1 Each joint angle at the p-th and p+1-th iterations is shown.

2. The method for obstacle avoidance inverse kinematics of a multi-joint manipulator based on damped least squares according to claim 1, wherein the second step is specifically:

2.1 According to the relative position relation between the barrier and the connecting rods in the multi-joint mechanical arm and the coordinate conversion relation of the positive kinematics of the multi-joint mechanical arm, calculating the acting direction of virtual repulsive force of each barrier to each connecting rod in the multi-joint mechanical arm and the corresponding virtual repulsive force potential energy;

2.2 Multiplying the action direction of virtual repulsive force of each obstacle to the current connecting rod in the multi-joint mechanical arm by the corresponding virtual repulsive force potential energy to obtain virtual repulsive force of each obstacle to the current connecting rod in the multi-joint mechanical arm, and summing the virtual repulsive forces to obtain the total virtual repulsive force of the obstacle to the current connecting rod in the multi-joint mechanical arm;

2.3 Repeating 2.1) -2.2), calculating and obtaining the total virtual repulsive force of the obstacle to the rest connecting rods in the multi-joint mechanical arm.

3. The method of inverse kinematics for obstacle avoidance of a multi-joint manipulator based on damped least squares according to claim 2, wherein the direction of the virtual repulsive force of the respective obstacle to each link in the multi-joint manipulator is determined by the relative position between the obstacle and the link, in particular:

for the action direction of virtual repulsive force of the obstacle k to the connecting rod i, the geometric center O of the obstacle k and two end points P of the connecting rod i _A 、P _B Distance OP between _A 、OP _B Two end points P of the connecting rod i _A 、P _B Connected to form an axis P _A P _B The relationship between them is divided into the following three cases:

when the geometric center O of the obstacle k is at the axis P of the connecting rod i _A P _B Projection onto P _B On one side of the extension line, the distance d between the obstacle k and the connecting rod i is in space _ik Satisfy d _ik ＝|OP _B |-R-r _k R is the radius of the circle where the end part of the connecting rod i is positioned, R _k Is half of the maximum diameter of the obstacle, the virtual repulsive force acts in the direction of

When the geometric center O of the obstacle k is at the axis P of the connecting rod i _A P _B Projection onto P _A On one side of the extension line, the distance d between the obstacle k and the connecting rod i is in space _ik Satisfy d _ik ＝|OP _A |-R-r _k The virtual repulsive force acts in the direction of

In the geometry of the obstacle kThe heart O being at the axis P of the connecting rod i _A P _B The projection on the axis P _A P _B The distance d between the obstacle k and the link i _ik Satisfy d _ik ＝|OP _v |-R-r _k The virtual repulsive force acts in the direction of

4. The method for obstacle avoidance inverse kinematics of the multi-joint mechanical arm based on damping least square according to claim 2, wherein the calculation formula of the virtual repulsive force potential energy of each obstacle to the current connecting rod in the multi-joint mechanical arm is as follows:

wherein E is _ik Representing the virtual repulsive potential energy of an obstacle k acting on a connecting rod i _r For the repulsive force coefficient of the obstacle, d ₀ Distance of influence of obstacle d _ik Is the spatial distance of obstacle k to link i.

5. The method for obstacle avoidance inverse kinematics of a multi-joint mechanical arm based on damping least squares according to any one of claims 1-4, wherein adjacent links of the multi-joint mechanical arm are connected by adopting universal joints.